Paul - Welcome to the forum. I'm 10 minutes east of you. Ocean State Job Lot on Jericho Tnpk in East Northport usually has liquid chlorine at 12.5%. That is where I purchased mine. When I bought my house with a pool, I inherited the pool company from the prior owners. I watched them and paid them the first year and they didn't do much for the money I was paying them. I joined this forum and did a lot of reading. The second year, I fired the pool company and have done everything myself ever since. It's been 7 years since then and my pool has been pristine ever since.
Couple key things you should be aware of if you're going to start this journey and do it correctly:
Number 1 is testing your own water with a proper test kit. Don't trust other's tests. Period. Don't mix and match advice. You're either going to follow the main tenets outlined here or you're going to do your own thing. Jumping around from one approach to another is only going to set you back and confuse your program for water management. You'll need to figure out which avenue you're going to go down. We can help anyone who is willing to listen and follow the protocols.
Number 2 is chlorination and chemicals. We only want to add what the water needs. Your testing will tell you what the water needs. Right now, it seems you need chlorine, and lots of it. You need to maintain SLAM as religiously as possible until all 3 criteria are met. You should also be brushing, vacuuming, and cleaning your filter regularly to expedite the process of removing the algae. Adding pucks is going to raise your CYA. As others have indicated, with a FC reading over 10, your PH reading is no longer valid. No need to test for that during a SLAM. If you keep your FC high enough for your CYA level, everything else is easy. Leslie's recommendation of FC level between 1 and 4 is wrong. CYA matters and is key to the proper management of pool sanitation.
Number 3 is the question of who is going to manage the pool. If you're giving the pool guy the responsibility (and a considerable amount of money), then you're not going to be able to manage the pool using the advice here. He's going to add what he wants, and do what he thinks is best. You have a good test kit, and you have extremely talented and experienced people here willing to assist you and guide you. You'll need to choose the correct path that works for you right now. If you don't have the time or the patience to read, learn and follow the expert recommendations provided on this forum...that is OK. Just know that we'll be here for you if the new pool service doesn't work out.
Number 4 is pool opening and closing. I close my pool in late October and open in early April. Why? When pool water temps get above 60 deg F, algae can grow more easily. If you wait until memorial day to open the pool, your water temp is likely in the 70s. I open to a clear pool every season, as do most folks here who close late and open early.
This isn't rocket science, and I can tell you from experience that I have never found a nicer, more helpful bunch of people on the internet than those you will find here on this forum. There are lots of other tips here that you will discover if you read enough and take the time to learn. Good luck with whatever approach you choose.